1. What is the 2D Distance Formula?

The 2D distance formula calculates the straight-line distance between two points in a Cartesian coordinate system. It's derived from the Pythagorean theorem and is fundamental in geometry, physics, and computer graphics.

2. How Does the Calculator Work?

The calculator uses the distance formula:

Where:

• \( (x_1, y_1) \) — Coordinates of the first point
• \( (x_2, y_2) \) — Coordinates of the second point
• \( d \) — Distance between the points

Explanation: The formula calculates the hypotenuse of a right triangle formed by the differences in x and y coordinates.

3. Applications of Distance Calculation

Details: Used in navigation systems, game development, computer vision, physics simulations, and any application requiring measurement between points in 2D space.

4. Using the Calculator

Tips: Enter coordinates for both points. The calculator works with any real numbers (positive or negative). Results are rounded to 4 decimal places.

5. Frequently Asked Questions (FAQ)

Q1: Does the order of points matter?
A: No, distance is the same whether calculated from point A to B or B to A.

Q2: What units does this use?
A: The result is in the same units as your input coordinates (pixels, meters, etc.).

Q3: Can this be extended to 3D?
A: Yes, the 3D distance formula adds a z-component: \( \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \).

Q4: How accurate is this calculation?
A: It's mathematically precise, though floating-point arithmetic may introduce tiny rounding errors.

Q5: What about non-Euclidean distances?
A: For Manhattan/taxicab distance, use \( |x_2-x_1| + |y_2-y_1| \).